Ross Stewart scored at both ends for the Black Cats, who came from behind to win.
Stewart headed Tyler Morton's free-kick into his own net to give Rovers an early lead.
Stewart scored a penalty and won the game two minutes later.
It looked as though the points would be shared until a free- kick was missed by Blackburn.
Patrick Roberts' drive was charged down by Bradley Dack, who was playing for the Black Cats.
Stewart diverted the ball over the line after Morton delivered a free-kick from the left, but the goal was ruled out for a foul.
The referee awarded a penalty after Stewart fell under John Buckley's challenge, after the home side worked the ball into the penalty area.
The Scotland international stepped up to slam the equaliser past Thomas Kaminski and the Wearsiders looked like they were going to take the lead with a chance that Roberts dragged wide.
Stewart had a chance to score again after the break, but he missed his shot at Kaminski.
The home side continued to threaten going forward and they were able to make a few saves.
At the other end, Dack's through-ball set up an opportunity for Morton, but Anthony Patterson tipped his effort over the goal line.
After winning the second ball from O'Nien's free-kick, Simms calmly slotting into the bottom corner for his third goal of the game.
With 24 matches played, Rovers are yet to record a single draw this season.
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